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Full text of "The riveting of aluminum and its alloys."

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ALUMINUM COMPANY OF AMERICA • PITTSBURGH.PA. 



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< <»n RIGHT 1984 

\l ! MIM M COMPANY 



<>i \\ii-.iu<:\ 



the mvi:n\4. OF 



ALUMINUM 



AND ITS ALLOYS 



* 





iveting is a very satisfactory method of joining Alcoa Alu- 
minum and its alloys. Rivets made from various aluminum 
alloys are employed in aluminum structures where maximum 
corrosion resistance and weight saving are essential. However 
aluminum structures which are to be painted may be joined with 
ordinary steel rivets. The following aluminum alloys are most 
commonly used for rivets: 2S (commercially pure aluminum), 3S, 
4S, ITS and 5 IS. 

Rivets of 2S, 3S and 4S are formed from wire or rod stock 
w hich has been cold worked to an intermediate temper. As the 
properties of these three so-called common alloys are not im- 
proved by heat treatment, rivets made from them are always 
driven cold in (he "as-received" condition. The other two alloys 
(ITS and 5 IS), known as strong alloys, have their properties im- 
proved by heat treatment and consequently, rivets made from 
them should always be heat treated* before or during the driving 
operation as will be explained later. 

Aluminum alloy rivets are furnished in a number of types. 
Button, round, mushroom, brazier, and flat head rivets are fur- 
nished with a small fillet at the junction of the shank and head. 
The radius of this fillet is equal to about one-tenth of the shank 
diameter with a minimum of 0.01 inches. 

•The li'Ml irfMlmenl of ">1S is covered by patents owned by Aluminum Company of America. 



6 



THE KIVKTING OF ALUMINUM 



THE STRENGTH OF RIVETED 

JOINTS 




\ a property designed riveted joint, rivets are spaced so that 

I he force acting on any individual rivet does not exceed the 

safe design \alue oi ihe rivet. Safe design values are given in 

shear, tension and bearing (crushing). They are determined in 

such a way that an ample margin of safely is provided againsl 

ich of the three corresponding t\pes of failure. 



Safe Shear Value of Rivets: — The first consideration in Ihe 
selection of the proper rivet is its shear strength which depends 
upon : 

1. Its cross-sectional area. 

2. The shearing strength of the material. 

3. The Dumber of planes along which the rivel (ends to shear; 

viz., single shear, double shear. 

The cross-sectional area of a driven rivet is an uncertain 

quantity because hole sizes vary. In addition, when (lie rivel is 

Upset the size of the hole is general I \ increased by the swelling 

action of the rivet. Some engineers use the nominal diameter of 
the rivel for calculating areas and others use the diameter of the 
hole. In mosl cases it seems unnecessarily conservative to 1 i 
alculations on the nominal diameter of the rivet <m(\ therefori 
it is i ►mmended I hat the hole diameter be used, up to a limit ing 

value 5 per cent greater lhan the nominal diameter of the rivet. 
In general, the nominal shearing strength of the rivel ma- 
terial is i good ba-i^ for calculating the shearing strength of 
driven rivets. Actual tests on driven rivets, however, have in 
diiatcd that in some cases ihe driving operation increase Mi 
shearing strength. Advantage hag been tal n of thi^ fa< i in lh 




lion of the design st re 



^ 



:i\ en in Tal I 



'I he number of planes on w hich a ri\ el tends to sh( ar depend 
tire|\ on the design of the joint. Inmost cases, rivet ur< use* 



VLVMIMM COMPANY OF AMERICA 



7 



TABLK I— S 



SHK-VRING DESIGN STRESSES FOR RIVETS 



These values have a factor of safety of about 3.5 based 

on tests of driven rivets. 



Rivet 



2S 

3S 

4S 
17S 



51S-W 



17S 
51S 
Steel 




Cold As-received 

Cold As-received 
Cold As-received 
Cold immediately 
after quenching 
Cold As-received 



Hot 930° to 950°F. 
Hot 960° to 980°F. 
Hot 1700° to 1900°F. 



Safe Shearing 

Design Stress, 

Ll>-. per square inch 



3 , 000 

4,000 

5,500 

10,000 

8,000 



9,000 

6,000 

13,000 



TABLE II— SAFE DESIGN VALUE OF ONE RIVET IN 

SINGLE SHEAR, LBS. 

Factor of safety of about 3.5 based on tests of driven rivets. 
Diameter of hole assumed 5 per cent greater than diameter of rivet 
For double shear values, multiph by two. 



Size, 


Cold Driven 


Hot Driven 


inches 


2S 


3S 


4S 


17S* 


51S-W 


17S 


51S 


Steel 


H 
1 


160 
370 
650 

1,010 
1,460 
1 , 990 


220 

490 

80(1 

1,350 

1,940 

2,660 


300 

670 

1,190 

1 , 860 

2,670 


540 
1 , 220 
2,160 
3,380 

* # . * • 
9 m • ■ • 


430 

980 

1 , 730 
2,710 
3,900 


■ • * m 

1,100 
1,940 
3 , 040 
4,370 
5,980 
7,790 


730 
1,300 
2 , 030 
2,920 
3,980 
5,190 


700 
1,590 
2 , 800 
4 , 400 
6,320 
8,630 
1 1 , 250 



*Dri\pn immediately after quenching. 



V I : 



































VLl MINI M COMPANY OF AMERK \ 




Safe Tensile Value of Rivets: — Rivets are not well -uited 
for transmitting loads in tension because a slight eccentricity of 
load exerts a prying action on the head which may result in an 
early failure. This tendency is especially marked under the con- 
dition of repeated loads. For this reason, it is generally accepted 
design practice to avoid the use of any connection designed prin- 
<i pally for transmitting loads by tension in the rivets. Tensile 
>l tosses in rivets cannot always be avoided because racking of I he 
framework and other secondary effects may produce appreciable 
tensile loads. In such cases the safe tension value of a rivet ma> 
be taken as one-half the safe single shear value. (See Tables I and 
II.) In all cases an effort should be made to keep such secondar\ 
tensile stresses in rivets as small as possible. 

Safe Bearing Value of Rivets: — The bearing value de- 
pends upon: 

1. The area in bearing. 

2. The bearing strength of the metal in the rivet or plat* 
whichewr is the smaller. 

3. The edge distance in the direction in which the joint i- 

stressed. 

The area in bearing is the thickness of metal times the di- 
ameter of hole. It is recommended that for calculating bearing 
areas the hole diameter be taken not greater than 1.05 times the 

nominal rivet diameter. 

The ultimate bearing strength of aluminum alloys in contact 
with driven rivets is about 1.8 times the nominal tensile strength 
of I he metal, provided the edge distance in the direction of stress- 
ing is equal to at least twice the diameter of the hole, edge dis- 
tance being measured from the center of the hole. For smaller 
edge distances the bearing strength drops oil about in proportion 
to the decrease in edge distance, so that for an edge distance of 
one and one-half diameters the bearing strength is about three- 
quarters of that for an edge distance of two diameters. 

Hearing tests of joints show that the first appreciable perma- 
nent distortion of the hole occurs when the bearing stress is 
about equal to the nominal tensile strength of the material and 







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ALUMINUM COMPANY OF VVIERICA 



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that this yielding is practically independent of the edge distance. 
The safe bearing design stresses for various aluminum alloys 
gh en in Table III have an adequate factor of safety against both 
hole distortion and ultimate failure. 

Safe bearing stresses for driven rivets are given in Table IA 
and are to be used only when the rivet is softer than the material 



Ihrough which it is driven. For instance, if Y± inch 4S-J^H 
plates are joined by Yi inch 4S rivets driven in % inch diam- 
eter holes spaced \ Y /i inches from the edge of the plates, the safe 
bearing value is governed by the rivets and is 1830 lbs. (1.05 
x Vi * 34 x 14,000). If the same rivets are used in 4S-0 plates the 

safe bearing value is governed by the plates and is only 1440 lbs. 

i 



x 11,000). In the first case, if the edge distance 
inch, the plate would have governed and the 

7 ' 

v alue would have been 1620 lbs.f 1.05 x^x^x 15,000 x 




(1.05 x y 2 x 
had been only 




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32 




Riveting Aluminum Alloy Tank, % in 



Hot 51S-VV Rivets 



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llll Kl\ II IM. Ill \l I MIM M 



DESIGN PROPORTIONS Ol 

KIN Kill) JOINTS 




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i . Jim. tiMiii of ri\<'i< »l joints is thai the) l>< stron 

h transfer ^ . 1 1« • I \ the forces acting <>n ih< i parts 
hi i I Im requirement is responsible onl) in ;i verj general 

In d< .'ii oi the i in because number of joints can be 

n . nil strong iii^'li luii varying wide!) 
i in- ol ri\< i- In 1 1 M - following paragraphs the fa< 
i hi ral design "I riveted joints are discussed 

I I I ■ unci helpful in laying oul highl> stn ed joinl 

win. 1 1 i In rivet > in used simpl> l i i I il< h I ^ <• 






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ALUMINUM COMPANY OF AMERICA 



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joints this becomes the controlling consideration. The maximum 
spacing of rivets is determined only by the designer's sense of 
proportion, especially, in cases where the rivets are used simply 
to stitch two or more plates or shapes together. As a general rule 
it is recommended that the minimum distance between centers of 
rivets be not less than three times the nominal diameter of the 
rivet and the maximum distance be not greater than twenty-four 
times the thickness of the sheet or plate. 



Edge Distance 




— It has already been pointed out that for 
maximum bearing strength, the edge distance measured from the 
center of the hole in the direction of stressing should be at least 
l wice the diameter of the rivet hole and that the allowable bearing 
stress is decreased if the edge distance is less than this amount. 
Vside from considerations of strength, the edge distance is im- 
portant because of the possibility of bulging the edge of the 
plate, thereby producing poor appearance in the finished joint. 
Such bulging may be avoided by maintaining an edge distance of 
at least one and one-half times the diameter of the rivet and by 
exercising some care to avoid overdriven rivets. When edge 




Riveting; \luminum Alloy Crane Girder, V A *"• Hot Steel Rivets 






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AH MINIM COMPANY OF AMERK V 15 



DRIVING PROCEDURE 
FOR RIVETED JOINTS 

rpiHE driving procedure for riveted joints in aluminum alloy con- 
struction does not differ greatly from that used in similar con- 
st met inn involving other metals. The following paragraphs will 
explain the driving methods recommended for rivets of the va- 
rious materials and will discuss certain precautions which should 
be observed. 




2S. 3S and 4S Rivets: — These rivets are always driven cold 
in the "as-received" condition. They may be stored indefiniteh 
without affecting their strength or driving characteristics. 

17S Rivets: — ITS rivets should always be heat treated to pro- 
duce maximum properties. The heat treatment consists of holding 
the rivets at a temperature of 930°F. t<5 950°F. for a period of 
5 to 30 minutes, depending on the size and number, and then 
quenching immediately in cold water. Following this operation 
the rivets harden gradually, obtaining their full properties in 
about four days if kept at room temperature. During the firsl 
one or two hours immediately after quenching, the rivets are fair- 
l> soft and may be driven cold in sizes as large as Y% to % i n c h 
depending upon the shape of head and equipment available. 

If ITS rivets are allowed to age more than two hours at room 
temperature after quenching, they are generally too hard to drive 
and must be reheat treated. Reheat treatment is not injurious to 
the rivets and may be repeated as often as desired. In this con- 
nection it should be pointed out that the aging can be retarded 
very noticeably by storing the quenched rivets at low tempera- 
tures. Rivets stored at 32°F. immediately after quenching remain 
soft enough for driving for about 3o hours. By using solid C0 2 
( Hr\ Ice) much lower storage temperatures can be maintained 
and the driving period prolonged almost indefinitely. Vt a tem- 
perature of — 50°F. rivets remain soft enough for driving for a 
period of two weeks or more. 






I IH KIN I I l\«. <H VI 1 MIM VI 



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ITS rivets an usual! \ «Im\ en no 
I i,, • o°l hi he usual hrai in iting opei a 

1 1. •<! in i Ik boh 1 1 1 < I driv en Phe quern li i 
i it h I Ik relat i> el> cold dri> iiift tools and 
li i hi uportant I hat t he i i> els !►< 1 1 ans 

. :i t ul driven with a minimum laps** 
1 1,« ,| iu < M«-< i ami i" make 1 1 

! unlM.it li-.n' In 1 1 i i.il. I 7 V rivi I 

n the ( till s 1 1 • . * t I real ed n indil i ITS I 

i I In- i .in In- detei 1 1 (I l»\ I he 
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VLl MINI \l COMI'VW OF WIIHK \ 



17 



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to drive at random ral her than in succession. In some cases ii may 
In- necessary i<> cool l>> means of water or compre •! air pn f- 
erabl> the latter. In qo case should the temperature of th< 1 1 < j - 
minimi allo\ paris be allowed i«» rise above ^50 F. Ii ih pre- 
cautions are followed, the strength <>l the aluminum alio} part 

will not be affected and wurpin.u will be reduced to a minimun 

Pressures Required to Drive: — I I »• • f)ressure ' [uired to 
drive rivets depends upon I la- 9ize, i be type of head, tin- n d 

m ilie rivets, and the driving temperature If vari roughly a 
the square of i h < • diameter of the finished dim m h» id, that i 
small head has a considerable advantage over a largei one Tests 
have shown that I h« > standard button heal, il>< tmallesl i> 
how n on page <>. is larger than nerrssarj to devel p th< Jtrength 
of the rivet shank. Therefore, where ease of driving is import an I 
and w here a large head size is n< it needed foi appearance or oth 
reasons, il is recommended thai undersize ts b< used for th 
driven heads to decrease the required driving pr< sure 

Table \, page II. gives pressures i [uired to drive lull but 
tonheads with a squeeze riveter. This table rnay be used i i lid 
in comparing the driving characteristics of the dill-rent ri\ei 
md in selecting equipmenl for driving them. 

Riveting Equipment: — Squeeze riveters g< nei ill v are |> 
erable to other types f< »i driving rivets in aluminum. Their us 
assures proper I > upset shanks and well centered h< ids. 1 ' < 
pacit> required ma\ be determined b\ reference to Tal \ 

1 I 

Pneumatic hammers are suitable for riveting iluminum all<» 
structures provided the} are large enough to properly upsel th 
rivets. Driving tests on aluminum allo\ rivets indi< tie il 
various sizes of hammers will develop ihr following equivalenl 
pressures when used with aboul 90 lbs pei -«i in. air pressure 



H« >re and Stroke 
- if I lammer, 

inches 



I l l6 V 4 
1 l 16 \ <> 



Approximate 
Equi\ alent 

Pressure 



l\ Tons 

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I ;, -i . md Strol 
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irh hes 



l 1 X 

1 , V 

IS, x II 



Vpproxij te 
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18 I 



18 



THE RIVETING OF ALUMINUM 



These values may be used in conjunction with Table \ asa 
guide in the selection of equipment. Suppose it is desired to select 
a hammer for use on ]/ 2 in. 51S-W cold driven rivets. According 
to Table V this rivet requires 32 tons on a squeeze riveter for a 



< l 



complete button head, or about 22 tons {% of 32) if a completeh 
formed head is not required. Judging from the equivalent pres- 
sures given above, a hammer \ l u\ \ 8 or larger would be selected. 

The above values of equivalent pressure will be found some- 
what low when applied to hot driven steel rivets, probably be- 
cause steel rivets hold their heat better than aluminum alio} 
rivets during the driving operation. The size of hammers required 
for driving hot sleel ri\eis are too well known in fabrication shop- 
to require further comment. 

Aluminum alloy rivets may be headed by means of a hea\ > 
hand hammer or sledge. This method has been found ver\ 
satisfactory in locations which permit adequate bucking. His el 
sets for use on aluminum alios rivets should have smooth, polished 
surfaces so that the metal ma\ flow readil> during the formin 

of I he head. 

Heating equipment for steel rivets presents no new problem 
to the ordinary shop. For heat treating aluminum alloy rivets, 

reliable temperature indicator and good temperature control an 
essential. When ri\ets are to be quenched in waler for cold 
driving, the heating equipment generally consists of a ball) oi 
sodium nitrate heated b> gas. oil. or electricity. The rivets are 
handled in a l>a>ket made of wire mesh or perforated shed and 
-hould be quenched quickly after removal from the healing bath. 

Electrically heated air furnaces ma\ be used to heal rivets, pro- 
vided the temperatures are uniform throughout the furnace. \lu- 

minurn alios ri\ets for hot driving are generalh healed in a lead 
bath or in an electricalU healed air furnace. In both cas< 

the heating equipment must be near the work so that the time 
loss in transfer is minimized When heating in a lead bath, pro- 
vision must be made lo submerge the rivets in the balh. olhei 
wrise the) Boat. Ml adhering lead should he removed b\ a sharp 

hlnw of the tonj. 1 againsl some lid object, before the ri\< 
is inserted in ihe hole. 



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V ■ -I M1M M <OMP\\\ Oh VMKHK V 



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Kit<>i Hales: — Kivel hole> in aluminum alloys in.i\ be either 
punched, drilled, or sub-punched and reamed t<< size I he la>i 
method i^ prefers hie, especial!} if i he reaming is done in assembly 
to give the holes exacl coincidence, Ii has been foun<l that bridge 
reamers of the spiral -I luted type are the besl for use in aluminun 
ami aluminum alio} s. 

The clearance to allow in ifie f * • » l # - — depends lai l> on ti 
class <>l work Rivets, especially I hose cold driven, ar< ^i» r 
to <lits * - when the clearance iv small. II a loose lit is i d th 
rivel will be hard to hold straight ami e< i entric beads will often 
result. The best clearance is the smallest one which will all th 
rivel to be inserted easily withoul dela> lint rivets r< [uire i 

clearance ihan cold one- because the\ .n< harder i<> h indie. 



Rivet boles tend to gel out of coincidence during th< li 
operation because of slippage, swelling of the metal, and w irpin 
caused l>> heal. For ihis reason ihe work should be firml i 
semhled h> means of bolls before driving. Th( bolts mould b 
well lightened to prevenl slippage and il to prevent the rivel 
from squeezing oul between il parts of the joint. 



Lengths <>/ Rivets: — Hie length ol rivel requii I for [ 

a head depends upon I fie grip or h.tal thickness of m ftJ th _h 

which the rivel is driven, clearance between rivel and rivel boh 
the alloy, and the form of head Table \ I gh th( ngths for 
various grips for lull button heads on L7S rivets driven in 17S-1 
plate. The values in this table are curateonl) i"i the conditions 

slated but t he> ma> he used to estimate lengths 1 [Ui for other 

conditions. Because of variations in rivet sets and driving condi 
lions, the safest method to t'ollom i- i" make several trials wil 
the equipment to be used on ihe job lie tore spei ifying the t 

length of rivets. It is better to have the riv< _hi!\ long th i 

► short, because a short rivet ma\ , 1 1 b * v\ the rivel ri* 

and damage the plate. 



20 



THE RIVETING OF ALIMIMM 




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22 



THE RIVETING OF ALUMINUM 








« liri^ \lurriinij» \ll< l ru+r> 3 i in. 1 1 « » I ITS Riv«*t* 






ALUMINUM COMPANY OF AMERICA 



23 



SELECTION OF RIVET ALLOY 





he proper rivet to use in any aluminum alloy construction 

depends upon many factors, so that each individual applica- 
lion must be considered in the light of its own requirements. The 
following discussion covers some of the more general points in- 
fluencing the selection and presents certain combinations which 
have been found to be satisfactory. 

If an attempt is made to drive a hard rivet such as 17S into a 
soil plate such as 3S-0, the plate will be unduly distorted and the 
resulting appearance poor. In addition to this, the strength of 
the rivet is likely to be governed by its bearing value against the 
soft plate so that the shear strength of the rivet may be largely 
wasted. For these reasons it is poor policy to use a very hard 
rivet in a soft alloy. 

A soft rivet can sometimes be used to advantage in a hard 
alloy, especially if the joint is not highly stressed. It is generally 
advantageous to keep the rivet and structure of about the same 
properties. 

Steel rivets should never be used except where the finished 
structure is to be thoroughly painted and maintained, because 
rust stains are likely to mar the appearance if the bare steel is 
exposed. Properly protected steel rivets are satisfactory in many 
types of aluminum construction. 

The following combinations of structure and rivets have been 



found to work together very satisfactorily: 



Structure 



Rivets 



2S, nny temper W 2S 

3S-0, 4S-0 3S 

:{S or 4S, quarter hard or harder ;> +S. ~>l s -\\ 

A17S-T, 17S-T, 27S-T ITS. Steel 

.->1S-W ", 51S-T, 53S-W , 53S-T 4S, 51S-W, Steel 



1 



24 



THE RIVETING OF ALUMINUM 






AIRCRAFT RIVETING 



K 



iveting in aircraft construction is limited to the smaller sizes 
of rivets and consequently is nearly always done cold. The 
mosl commonly used rivel is ITS driven immediately after 
fiing as alread> described. These rivets de\elop an ultimate 



shear strength, based on the area of the hole, of 35.000 lbs. per sq. 
in. about 1 days after being driven. 

\\ here a higher shear strength than that of ITS is needed, 2 IS 
vets are used. Driven immediately after quenching from a tem- 
perature of o|o°F. to 930°F., the> develop an ultimate shear 
st ^th of about 11,000 lbs. per sq, in. based on the area of the 
hole, within about one day. Since the rate of age-hardening of 
_ \S rivets is more rapid than that of ITS rivets it is necessary to 
drive them more promptly after quenching. Experience indicate 
that the elapsed time should not exceed about 20 minutes. 

V17S-T rivets driven in the full} heat-treated condition, are 
ii< i in i' - used in aircraft construction to avoid the heat treatin 
involved in the use of L7S and 2 IS rivets. These rivets develop an 
ultimate shear strength, based on the area of the hole, of 28 000 
II pei sq. in. The> are slightly easier to drive than ITS rivet 
and \ (i > much easier to drive than 24S rivets. 

When Uclad 1TS-T or Uclad 2 IS- F is used, rivets of any of 

the above three alloys arc satisfactory since the \lclad coatin 
trolyticall) protects the heads of the rivets as it do. the cut 
of the sheet. I nder severeh corrosive conditions, however, 

W 

maj l idvantageous to use 5 1 S- W rivets with Vlclad alloys if 



tie ultimate -hem- strength of 51S-W, 28,000 lbs. per sq. in. 
►Id driven) is sufficient for the joints in question. Vs the 5 IS W 
rivet lead- much closer in electrical potential to the pur< 

aluminum coating than either ITS or 248 thej require less pro- 
tection and hence insure longer life to the coatin- in the vi< init) 

of ihc ri\ i 

Rivets to t used with Vlclad allov- an ometirm ordered 



w it h burnished heads s to 
Vlclad coating 



match more near! s i he color of t h 





ALUMINUM COMPANY OF AMKRICA 



2: 



i 



I 



TABLF VII— WEIGHT* OF BUTTON HEAD 

ALUMINUM ALLO\ RIVETS 

Values ^ivcn in pounds per hundred rivets 



Length 

I 'nd< 1 
I Ic;kI, 

inches 



(t 



l A 



1 



I 



H 
1 



; 



7 s 






J4 



0.2 

1 
5 
i) (i 

6 

(i 7 

(I s 

II s 

i) 9 

11 9 

t 

1 l 



I 



I 

2 



I 
I 



I 



I 
I 4 

1 5 

1 ii 
I 6 



I 
I 



I 

7 



I 8 

1.9 

1 9 

2 
2 
2 1 

2 
2 2 

2 I 

2 1 

2 5 

2 5 

2 «; 



Diameter in in< Ii 






0. 1 

• • • 

ll !) 

I 

I 1 

I ' 

1 I 

I t 

I s 

I (i 

I 7 
I 8 

1 9 

2 

2 11 

2 1 

2 ■ 
2 

2 1 

1 5 

2 ii 

2 7 
2 8 

2 9 

:i i) 

3 l 
3 

3 
3.4 

3 5 
8 6 
3.7 
3.8 

3 9 

4 
1 I 

12 



2 7 4 3 



« 



6 

■ • ■ 

1 1 
I ii 

1 7 

I !) 

e H 



2 

2 

> 
2 



I 

ii 



2.7 

2 8 

3 'I 
3 I 
3 

3 1 

3 .7 

3.7 

.; s 

3 'i 

I- I 



I 

1 



2 



4.6 

4 

1.9 

5 I 

.7 
5 



5 
5 



6 



5 8 

5 9 





7 /f 6 



II !) 



2 2 

2 1 

2 6 
2 

11 

3 2 

3 t 

3 6 

8 

:i 9 
1 l 

4 ! 
1 5 
I 7 

4 9 

5 1 

5 | 

.7 5 
5 7 

5 s 

6 

ii 

ii 4 

ii 6 

.; s 

7 11 

7 

7 i 

7.6 

7.7 
7 9 

s 1 

s 3 



6 2 8 .", 




1 1 



3 1 

3 6 

3 9 

1 I 

\ 4 

I <> 

I 9 

5 I 

5 I 

:> 6 

9 

6 1 

ii I- 

6 i; 

6 9 

7 1 



7 

m 

7 



6 

8 



s l 

8 I 

8 6 

8 8 

9 1 

9 I 

'. i; 



in 
10 



s 
1 
3 



10 ii 

10 s 

11 1 
11 



H 






1 

7 
7 

7 

8 
8 
9 

9 
9 

in 
in 

11 
11 
11 
l I 

I I 
I 3 
13 
13 

1 1 
1 1 
14 

17 
1.7 

16 
16 
16 

17 

17 

18 
18 

is 




2.8 1 8 



I I 
12 

I I 
I : 

I I 

1 1 

15 

15 

16 

17 

17 
Is 

18 

19 

in 

20 
20 

21 

2 2 

: I 
IS 

24 

2 1 

2 5 

2 5 

27 
27 



7 4 



7.6 



W eights given are for 17S. 

or 2S multiply 1>> 0.971 For 8S mult ipl\ h> n.98 I 



18 
19 

20 

21 
21 

24 
li 

26 

27 

2 7 

28 

!■> 
.in 

30 
31 

34 

■ 

36 

36 



1 



1 I :; 



31 
32 

34 

35 
36 

n 

38 

10 
41 

12 

13 
44 

r> 

46 

17 

is 

1" 
50 

51 



*H 



Hi 



1 



to 

n 

1.' 

44 

r, 
n; 

17 
49 
50 
51 

56 

58 

i;n 
61 



IX 



" I 



58 

61 

■ 

■ 

■ 

79 
81 

^1 



Fof .71S multiply [>\ 0.965. 



; -r I s * multipk l>\ -~ " 



M I I 



\ \| I V 



- \l I 



■I I h 









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